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Maths II

Compound interest and appreciation/depreciation

With **simple interest** the amount of money borrowed remains fixed.

For example £400 is borrowed for 3 years at an interest rate of 5% pa (pa means **per annum**, or each year).

Interest for one year = 5% of £400

=

=

Interest for 3 years =

You can write this in a formula.

- P (principal) is the amount borrowed.
- R is the rate of interest per year.
- T is the time in years.

Here the interest is added to the principal at the end of each year. So the next year the interest is worked out on a larger amount of money than what was originally borrowed.

This means paying interest on the interest of previous years (unlike simple interest, where you only pay interest on the original amount).

This is how it is calculated:

£400 is borrowed for 3 years at 5% compound interest.

Principal at the start = **£400**

Interest in the 1st year =

Principal after 1 year = **£420**

Interest in the 2nd year =

Principal after 2 years = **£441**

Interest in the 3rd year =

Principal after 3 years = **£463.05**

The total interest charged under compound interest will be **£63.05**.

This is different to the simple interest worked out above.

In percentage questions, read the question carefully and decide what you are being asked to do. You may need to:

- Find a given percentage of an amount.
- Work out a percentage when given 2 amounts.
- Work backwards from a percentage increase or decrease (reverse percentages).
- Find a cumulative change.

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